Presuming the first husband was not Catholic, and further presuming that the marriage was not celebrated before a priest, there would be no need for a Declaration of Nullity because they would not be considered duly married in the eyes of the church.
I don't know if it's up to each diocese or what, or whether you are reading very old Canon law (the Council of Trent that you cite is 16th century, and there have been a multitude of changes since then, like it or not).
There is most certainly a procedure for what is commonly called an anullment, officially called a Declaration of Nullity. The grounds basically are described as that there was no "real" marriage in the first place, and it has been variously defined according to each case.
It's not always granted, but it is most certainly granted at present more often than it was granted in the 16th century.
These are several wild assumptions without evidence. OTOH, it is a matter of public record that she was divorced and living with another man without benefit of marriage.
I don't know if it's up to each diocese or what, or whether you are reading very old Canon law (the Council of Trent that you cite is 16th century, and there have been a multitude of changes since then, like it or not).
The citation is a matter of Catholic Dogma. It is part of the faith, and is perfectly clear in the Gospels.
And He said to them, "Whoever divorces his wife and marries another woman commits adultery against her; and if she herself divorces her husband and marries another man, she is committing adultery." (St. Mark 10.11-12)
The grounds basically are described as that there was no "real" marriage in the first place, and it has been variously defined according to each case.
Adultery is not one of the grounds.